The electric field in a region depends only on \( x \) and \( y \) coordinates as \( \vec{E} = k \frac{x \hat{x} + y \hat{y}}{x^2 + y^2} \) where \( k \) is a constant. The flux of \( \vec{E} \) through the surface of a sphere of radius \( R \) with its center at the origin is \( n\pi k R \), where the value of \( n \) is ___ (in integer).